Diffusion Tensor Magnetic Resonance Imaging (DTI) is a well known technique that can provide information about the neuronal fiber structure of the brain. However, since DTI requires a large amount of data, a high speed MRI acquisition technique is needed to acquire these data within a reasonable time. Echo Planar Imaging (EPI) is a technique that provides the desired speed. Unfortunately, the advantage of speed is overshadowed by image artifacts, especially at high fields. EPI artifacts originate from susceptibility differences in adjacent tissues and correction techniques are required to obtain reliable images. In this work, the fieldmap method, which tries to measure distortion effects, is optimized by using a non linear least squares estimator for calculating pixel shifts. This method is tested on simulated data and proves to be more robust against noise compared to previously suggested methods. Another advantage of this new method is that other parameters like relaxation and the odd/even phase difference are estimated. This new way of estimating the field map is demonstrated on a hardware phantom, which consists of parallel bundles made of woven strands of Micro Dyneema fibers. Using a modified EPI-sequence, reference data was measured for the calculation of fieldmaps. This allows one to reposition the pixels in order to obtain images with less distortions. The correction is applied to non-diffusion weighted images as well as diffusion weighted images and fiber tracking is performed on this corrected data.